Convergence properties of the conjugate descent method. (English) Zbl 0871.49028

Summary: The conjugate descent (CD) method was introduced by Fletcher. This paper investigates its global convergence properties. We prove that a kind of inexact line search conditions can ensure the convergence of the CD method. Several examples are constructed to show that the CD method may fail if the search conditions are relaxed, which implies that our result can not be improved. In addition, we obtain a result on those methods related to the Fletcher-Reeves method.


90C52 Methods of reduced gradient type
90C99 Mathematical programming